Question
A ball was kicked from the ground with a velocity of 64 feet per second and followed the path modeled by the function: h(t)=−16t2+64t
.(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The vertex of the rock's path indicates the rock took Response area seconds to reach its maximum height of Response area feet. Looking at the graph of this function, we can see the domain in context to this situation is 0 to 4 because the ball
.(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
The vertex of the rock's path indicates the rock took Response area seconds to reach its maximum height of Response area feet. Looking at the graph of this function, we can see the domain in context to this situation is 0 to 4 because the ball
Answers
GPT-4o mini
To find the vertex of the function \( h(t) = -16t^2 + 64t \), which represents the height of the ball over time, we can use the formula for the vertex of a quadratic function \( t = -\frac{b}{2a} \).
In this function:
- \( a = -16 \)
- \( b = 64 \)
Calculating the time at which the maximum height is reached:
\[
t = -\frac{64}{2 \cdot -16} = -\frac{64}{-32} = 2 \text{ seconds}
\]
Next, we can find the maximum height by substituting \( t = 2 \) back into the height equation:
\[
h(2) = -16(2^2) + 64(2) = -16(4) + 128 = -64 + 128 = 64 \text{ feet}
\]
Thus, we can fill in the blanks in the sentence:
The vertex of the rock's path indicates the rock took **2** seconds to reach its maximum height of **64** feet. Looking at the graph of this function, we can see the domain in context to this situation is 0 to 4 because the ball **returns to the ground (height = 0)**.
In this function:
- \( a = -16 \)
- \( b = 64 \)
Calculating the time at which the maximum height is reached:
\[
t = -\frac{64}{2 \cdot -16} = -\frac{64}{-32} = 2 \text{ seconds}
\]
Next, we can find the maximum height by substituting \( t = 2 \) back into the height equation:
\[
h(2) = -16(2^2) + 64(2) = -16(4) + 128 = -64 + 128 = 64 \text{ feet}
\]
Thus, we can fill in the blanks in the sentence:
The vertex of the rock's path indicates the rock took **2** seconds to reach its maximum height of **64** feet. Looking at the graph of this function, we can see the domain in context to this situation is 0 to 4 because the ball **returns to the ground (height = 0)**.